GRADE 4 - TEKSing toward STAAR -...

TEKSING TOWARD STAAR © 2014

GRADE 4Open-Ended

Problem-SolvingProjections

Organized byTEKS Categories

®MATHEMATICS

TEKSING TOWARD STAAR

TEKSING TOWARD STAARGRADE 4 PROBLEM-SOLVING PROJECTIONS

Table of Contents

TEKSING TOWARD STAAR 2014 Page 1

Mathematical Process Standards

These student expectations will not be listed under a separate TEKS category.Instead, they will be incorporated into questions across TEKS categories since

the application of mathematical process standards is part of each knowledge statement.

(4.1) Mathematical Process StandardsThe student uses mathematical processes to acquire and demonstrate mathematical understanding.STAAR

Standard TEKS STUDENT EXPECTATION

Incorporatedinto 1-4

4.1(A) apply mathematics to problems arising in everyday life, society, and the workplace


4.1(B) use a problem-solving model that incorporates analyzing given information, formulatinga plan or strategy, determining a solution, justifying the solution, and evaluating theproblem-solving process and the reasonableness of the solution


4.1(C) select tools, including real objects, manipulatives, paper and pencil, and technology asappropriate, and techniques, including mental math, estimation, and number sense asappropriate, to solve problems


4.1(D) communicate mathematical ideas, reasoning, and their implications using multiplerepresentations, including symbols, diagrams, graphs, and language as appropriate


4.1(E) create and use representations to organize, record, and communicate mathematicalideas


4.1(F) analyze mathematical relationships to connect and communicate mathematical ideas


4.1(G) display, explain, and justify mathematical ideas and arguments using precisemathematical language in written or oral communication


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TEKS Category 2: Number and Operations

(4.2) Number and OperationsThe student applies mathematical process standards to represent, compare, and order

whole numbers and decimals and understand relationships related to place value.STAAR


Supporting 4.2(A) interpret the value of each place-value position as 10 times the position to the right andas one-tenth of the value of the place to its left

Readiness 4.2(B) represent the value of the digit in whole numbers through 1,000,000,000 and decimalsto the hundredths using expanded notation and numerals

Supporting 4.2(C) compare and order whole numbers to 1,000,000,000 and represent comparisons usingthe symbols >, <, or =

Supporting 4.2(D) round whole numbers to a given place value through the hundred thousands placeSupporting 4.2(E) represent decimals, including tenths and hundredths, using concrete and visual models

and moneySupporting 4.2(F) compare and order decimals using concrete and visual models to the hundredthsReadiness 4.2(G) relate decimals to fractions that name tenths and hundredthsSupporting 4.2(H) determine the corresponding decimal to the tenths or hundredths place of a specified

point on a number line

(4.3) Number and OperationsThe student applies mathematical process standards to represent

and generate fractions to solve problems.STAAR


Supporting 4.3(A) represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbersand b > 0, including when a > b

Supporting 4.3(B) decompose a fraction in more than one way into a sum of fractions with the samedenominator using concrete and pictorial models and recording results with symbolicrepresentations

Supporting 4.3(C) determine if two given fractions are equivalent using a variety of methodsReadiness 4.3(D) compare two fractions with different numerators and different denominators and

represent the comparison using the symbols >, =, or <Readiness 4.3(E) represent and solve addition and subtraction of fractions with equal denominators using

objects and pictorial models that build to the number line and properties of operationsSupporting 4.3(F) evaluate the reasonableness of sums and differences of fractions using benchmark

fractions 0, 1/4, 1/2, 3/4, and 1, referring to the same whole linesSupporting 4.3(G) represent fractions and decimals to the tenths or hundredths as distances from zero on

a number line


Table of Contents


TEKS Category 2: Number and Operations

(4.4) Number and OperationsThe student applies mathematical process standards to develop and use strategies and

methods for whole number computations and decimal sums and differencesin order to solve problems with efficiency and accuracy.

STAARStandard TEKS STUDENT EXPECTATION

Readiness 4.4(A) add and subtract whole numbers and decimals to the hundredths place using thestandard algorithm

Supporting 4.4(B) determine products of a number and 10 or 100 using properties of operations and placevalue understandings

Supporting 4.4(C) represent the product of 2 two-digit numbers using arrays, area models, or equations,including perfect squares through 15 by 15

Supporting 4.4(D) use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digitnumber. Strategies may include mental math, partial products, and the commutative,associative, and distributive properties

Supporting 4.4(E) represent the quotient of up to a four-digit whole number divided by a one-digit wholenumber using arrays, area models, or equations

Supporting 4.4(F) use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor

Supporting 4.4(G) round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutionsinvolving whole numbers

Readiness 4.4(H) solve with fluency one- and two-step problems involving multiplication and division,including interpreting remainders


Table of Contents


TEKS Category 3: Algebraic Reasoning

(4.5) Algebraic ReasoningThe student applies mathematical process standards to develop concepts

of expressions and equations.STAAR


Readiness 4.5(A) represent multi-step problems involving the four operations with whole numbers usingstrip diagrams and equations with a letter standing for the unknown quantity

Readiness 4.5(B) represent problems using an input-output table and numerical expressions to generatea number pattern that follows a given rule representing the relationship of the values inthe resulting sequence and their position in the sequence

Not Tested 4.5(C) use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or2l + 2w), including the special form for perimeter of a square (4s) and the area of arectangle (l x w)

Readiness 4.5(D) solve problems related to perimeter and area of rectangles where dimensions arewhole numbers


Table of Contents


TEKS Category 4: Geometry and Measurement

(4.6) Geometry and MeasurementThe student applies mathematical process standards to analyze geometric attributes

in order to develop generalizations about their properties.STAAR


Supporting 4.6(A) identify points, lines, line segments, rays, angles, and perpendicular and parallel linesSupporting 4.6(B) identify and draw one or more lines of symmetry, if they exist, for a two-dimensional

figureSupporting 4.6(C) apply knowledge of right angles to identify acute, right, and obtuse trianglesReadiness 4.6(D) classify two-dimensional figures based on the presence or absence of parallel or

perpendicular lines or the presence or absence of angles of a specified size

(4.7) Geometry and MeasurementThe student applies mathematical process standards to solve problems

involving angles less than or equal to 180 degrees.STAAR


Not Tested 4.7(A) illustrate the measure of an angle as the part of a circle whose center is at the vertex ofthe angle that is "cut out" by the rays of the angle. Angle measures are limited to wholenumbers

Not Tested 4.7(B) illustrate degrees as the units used to measure an angle, where 1/360 of any circle isone degree and an angle that "cuts" n/360 out of any circle whose center is at theangle's vertex has a measure of n degrees. Angle measures are limited to wholenumbers

Readiness 4.7(C) determine the approximate measures of angles in degrees to the nearest whole numberusing a protractor

Supporting 4.7(D) draw an angle with a given measureSupporting 4.7(E) determine the measure of an unknown angle formed by two non-overlapping adjacent

angles given one or both angle measures

(4.8) Geometry and MeasurementThe student applies mathematical process standards to select appropriate customary and metric units,

strategies, and tools to solve problems involving measurement.Supporting 4.8(A) identify relative sizes of measurement units within the customary and metric systemsSupporting 4.8(B) convert measurements within the same measurement system, customary or metric,

from a smaller unit into a larger unit or a larger unit into a smaller unit when given otherequivalent measures represented in a table

Readiness 4.8(C) solve problems that deal with measurements of length, intervals of time, liquid volumes,mass, and money using addition, subtraction, multiplication, or division as appropriate


Table of Contents


TEKS Category 5: Data Analysis

(4.9) Data AnalysisThe student applies mathematical process standards to solve problems by collecting,

organizing, displaying, and interpreting data.STAAR


Readiness 4.9(A) represent data on a frequency table, dot plot, or stem-and-leaf plot marked with wholenumbers and fractions

Supporting 4.9(B) solve one- and two-step problems using data in whole number, decimal, and fractionform in a frequency table, dot plot, or stem-and-leaf plot


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TEKS Category 6: Personal Financial Literacy

(4.10) Personal Financial LiteracyThe student applies mathematical process standards to manage one's financial resources effectively

for lifetime financial security.STAAR


Supporting 4.10(A) distinguish between fixed and variable expensesSupporting 4.10(B) calculate profit in a given situationNot Tested 4.10(C) compare the advantages and disadvantages of various savings optionsNot Tested 4.10(D) describe how to allocate a weekly allowance among spending; saving, including for

college; and sharingSupporting 4.10(E) describe the basic purpose of financial institutions, including keeping money safe,

borrowing money, and lending

TEKSING TOWARD STAAR ©2014 Page 1

OVERVIEWGrade 4 Open-Ended Problem-Solving Projections

The Open-Ended Problem-Solving Projections were created with all students in mind and provideteachers with large print projections for problem-solving questions that address all TEKS, includingthe Process Standards TEKS and the TEKS not assessed on STAAR. Each Problem-SolvingProjection is correlated to a specific Category and TEKS.The Open-Ended Problem-Solving Projections document includes a general set of questions thatshould be addressed by students as they solve the problems and during class discussion of thesolution process for each problem. Teachers should make a copy of these questions and distributefor each student to keep in their math notebook.

The Problem-Solving Questions include the following:1. What is the main idea of this problem?2. What are the supporting details in this problem?

3. What skills, concepts and understanding of math vocabulary are needed to be able to answer thisproblem?

4. Did this problem involve mathematics arising in everyday life, society, or the work place?5. What is a good problem solving strategy for this problem?

6. Can you explain how you used any math tools, mental math, estimation or number sense to solvethis problem?

7. Did this problem involve using multiple representations (symbols, diagrams, graphs, language)?8. Did you use any relationships to solve this problem?

9. How can you justify your solution?10. How can you check for reasonableness of your solution to this problem?

These Open-Ended Problem-Solving Projections can be utilized for instruction, guided practice orindependent practice. These materials can be utilized with a whole class, small groups and/or tutorialsettings.

NOTE: There is no answer key provided for the Open-Ended Problem-Solving Projections as theauthor's philosophy is that each teacher should create a personalized Solutions Manual so theteacher becomes more familiar with the Revised TEKS and assessment of the Revised TEKS, as wellas formulates various solution strategies for each question. Teachers are encouraged tocommunicate with the author regarding discussion of any question in this document.

®MATHEMATICS


TEKSING TOWARD STAAR ©2014 Page 2

AUTHOR'S VISION FOR IMPLEMENTATION - PROBLEM-SOLVING PROJECTIONS

Students work with partner pairs to answer the Open-Ended Problem-Solving Projections. Studentsrecord their work on notebooks paper.The teacher projects the problem, then sets a time limit prior to students’ beginning their work.Partner pairs are given specific “share” questions from 1-10 on the Problem-Solving Questions page.The process that should be followed by students for all Problem-Solving Projections is to answerquestions 1-3, then complete the solution to the problem, and finally answer questions 4-10.The teacher calls time and the partner pairs guide class discussion on their “share” assignments.Students who did not complete the solutions to the problem prior to the time limit must completetheir recording in a different color.

TEKSING TOWARD STAAR ©2014

Problem-Solving ModelStep Description of Step

1 Analyze the given information.Summarize the problem in your own words.Describe the main idea of the problem.Identify information needed to solve the problem.

2 Formulate a plan or strategy.Draw a picture or a diagram.Find a pattern.Guess and check.Act it out.Create or use a chart or a table.Work a simpler problem.Work backwards.Make an organized list.Use logical reasoning.Brainstorm.Write a number sentence or an equation.

3 Determine a solution.Estimate the solution to the problem.Solve the problem.

4 Justify the solution.Explain why your solution solves the problem.

5 Evaluate the process and the reasonablenessof your solution.Make sure the solution matches the problem.Solve the problem in a different way.

TEKSING TOWARD STAAR ©2014

Grade 4 Problem-Solving Questions

Directions:

Work with a partner.Write your answers on notebook paper.Answer questions 1-3.Complete the solution to the problem.Answer questions 4-10.

1. What is the main idea of this problem?

2. What are the supporting details in this problem?

3. What skills, concepts and understanding of math vocabulary areneeded to be able to answer this problem?

4. Did this problem involve mathematics arising in everyday life, society,or the work place?

5. What is a good problem solving strategy for this problem?

6. Can you explain how you used any math tools, mental math,estimation or number sense to solve this problem?

7. Did this problem involve using multiple representations (symbols,diagrams, graphs, math language)?

8. Did you use any relationships to solve this problem?

9. How can you justify your solution to the problem?

10. How can you check for reasonableness of your solution to this problem?


GRADE 4Open-Ended


TEKS CATEGORY 2

Number and Operations

®MATHEMATICS


TEKS Category 1 GRADE 4 TEKS 4.2G


4.2G Problem-Solving 1

The table represents the coins that three fourthgrade students put into their coin banks thisweek.

1. Write Corina's total amount as a decimal interms of a dollar.

2. Explain why Corina's total amount you wroteas a decimal is correct.

3. Write Corina's total amount as a fraction interms of a dollar.

4. Explain why Corina's total amount you wroteas a fraction is correct.

5. Write Jeff's total amount as a decimal interms of a dollar.

6. Explain why Jeff's total amount you wrote asa fraction is correct.

Coins in the BankQuarters Dimes Nickels Pennies

Corina 3 1 1 3Jeff 1 1 2 2Angie 2 2 0 1



7. Write Jeff's total amount as a fraction interms of a dollar.

8. Explain why Jeff's total amount you wrote asa fraction is correct.

9. Write Angie's total amount as a decimal interms of a dollar.

10. Explain why Angie's total amount you wroteas a decimal is correct.

11. Write Angie's total amount as a fraction interms of a dollar.

12. Explain why Angie's total amount you wroteas a fraction is correct.

13. How much will Corina have left if she spends63

100of a dollar? Show your work.

14. Explain how you know your answer toquestion 14 is correct.

Coins in the BankQuarters Dimes Nickels Pennies

Corina 3 1 1 3Jeff 1 1 2 2Angie 2 2 0 1



4.2G Problem-Solving 2

PROBLEM 1

The Whitney Library is 0.3 mile from school.

1. Ginger says after school she is going to walk3 tenths mile from school to the WhitneyLibrary. Does Ginger's statement makesense?

2. Explain your answer to question 1.

3. Nick says after school he is going to walk3 miles from school to the Whitney Library.Does Nick's statement make sense?


PROBLEM 2

Kent says he has8

100of a dollar in his pocket.

Marcus says that the decimal for8

100is 0.8.

5. What error did Marcus make?

6. What is correct decimal form for 8100

of a

dollar?



PROBLEM 3

Evie and Chandra saw this sign along thehighway during their vacation.

7. Eva says it is seventy-five hundredths of amile to Waterland. Does Eva's statementmake sense?


9. Chandra says it is seven and five-tenths ofa mile to Waterland. Does Chandra'sstatement make sense?


Fun Ahead!

Waterland

0.75 miles


GRADE 4Open-Ended


TEKS CATEGORY 3

Algebraic Relationships

®MATHEMATICS


TEKS Category 2 GRADE 4 TEKS 4.5B


4.5B Problem-Solving 1

Jeremy used green triangle pattern blocks tomake these four designs. The designs create apattern.

1. Make an input-output table to represent thenumber of each design and the number ofgreen pattern blocks in each design.

2. If he continues the pattern, how many greenpattern blocks will Jeremy use for his 6thdesign?

3. Explain why your answer to question 2 iscorrect.

4. How many green pattern blocks will Jeremyuse for his 9th design?


Design 1 Design 2 Design 3 Design 4



6. What is the rule for the pattern in Jeremy’sdesigns?


8. What is the sequence for the first five termsin this pattern?


Design 1 Design 2 Design 3 Design 4




PROBLEM 1

Bertie uses 9 yards to make 1 quilt. She bought162 yards of cotton fabric. She will use thefabric to make quilts.

1. Write an expression to represent the amountof fabric Bertie uses to make 1 quilt.

2. Explain why the expression is correct.

3. Write an expression to represent the amountof fabric Bertie bought.


5. Write an equation to represent the number ofcotton quilts, c, Bertie can make using thefabric she bought.

6. Explain why the equation is correct.



PROBLEM 2

Reagan bought 8 packages of party napkins.Each package has 8 napkins.

1. Write an expression to represent the numberof packages of party napkins Reagan bought.


3. Write an expression to represent the numberof napkins in each package Reagan bought.


5. Write an equation to represent the totalnumber of napkins, n, that Reagan bought.

6. Explain why the equation is correct.




One gallon of water is equivalent to 4 quarts ofwater. You can write a rule to represent thisrelationship.

PART 1

1. Write a rule to represent the relationshipbetween one gallon and four quarts.

Let g represent the number of gallons, theinput, and let q represent the total number ofquarts, the output.

PART 2

This is an input/output table representing therelationship between gallons and quarts.

Input Gallons g 1 2 4 6Output Quarts q

Use the rule you wrote in number 1 to answerquestions about the table.

2. How many quarts are in one gallon?

3. How many quarts are in two gallons?

4. How many quarts are in four gallons?

5. How many quarts are in six gallons?


GRADE 4Open-Ended


TEKS CATEGORY 4Geometry

andMeasurement

®MATHEMATICS


TEKS Category 3 GRADE 4 TEKS 4.7C


4.7C Problem-Solving 1

Your teacher will give you and your partner aprotractor to use to for this problem.

Andrew built two sets of stairs in his new house. Thesets of stairs are represented below.

1. Explain how to use a protractor to measure HGF .

2. What is the measure of HGF ?

3. Explain how you know the measure for HGF iscorrect.

4. Explain how to use a protractor to measure QRS .

5. What is the measure of QRS ?

6. Explain how you know the measure for QRS iscorrect.

7. What is the difference between the measure ofHGF and QRS ?

8. Explain why your answer to question 7 is correct.



4.7C Problem-Solving 2

These diagrams represent the tilt of the Earth'saxis in relationship to the sun in the NorthernHemisphere. The diagrams show the tilt of theaxis on the first day of winter, spring and fall,and summer.

Use a protractor to answer these questions.

1. In the Northern Hemisphere, Earth's axis istilted away from the sun on the first day ofwinter, which is often December 21.

Use a protractor to find the measure of themarked angle on the first day of winter, theshortest day of the year.

What is the measure of this angle?



2. Earth’s axis is not tilted away from ortoward the sun on the first days of springand fall, which are often on March 20 andSeptember 22.

What is the measure of the marked angleon the first day of spring or fall?

3. Earth’s axis is tilted toward the sun on thefirst day of summer, which is often onJune 21.

What is the measure of the marked angleon the first day of summer, the longest dayof the year?


GRADE 4Open-Ended


TEKS CATEGORY 5

Data Analysis

®MATHEMATICS





The students in a fourth grade class voted fortheir favorite ice cream flavor. They recordedthe data in a tally table, then counted the talliesto make a frequency table.

Favorite Ice Cream FlavorFlavor Tally Number

Vanilla 9

Strawberry 7

Chocolate 13

Banana 4

1. How many more students chose chocolate orvanilla than strawberry and banana combined?

2. Explain how you used the data to answerquestion 1.

3. How many students are represented in thedata?

4. Explain how you used the data to answerquestion 3.




Use the dot plot you and your partner created for4.9A Problem-Solving 2 to answer these questions.Answer the questions on notebook paper.

1. Which length of straws had the greatest number?

2. Which length of straws had the least number?

3. What is the difference between the number ofstraws with the least and greatest lengths?

4. What is the total number of straws that have a

length less than1

14

inch?

5. What is the total number of straws that have a

length greater than 11

4inch?

6. What is the difference between the number of

straws with a length less than1

14

inch and a

length greater than1

14

inch?

7. What is the difference between the number of

straws with a length of14

or12

in. and the

number of straws with a length of1

14

or1

12

in.?




Stephanie asked her 23 classmates how muchtime they spend doing chores in a week. Sherecorded the data in a stem-and-leaf plot.

1. How many classmates said they spend sometime doing chores in a week?


3. How many of Stephanie’s classmates saidthey spend more than an hour doing choresin a week?


Minutes Spent Doing ChoresStem Leaves

2 2 2 4 63 0 5 5 84 0 65 5 86 27 1 4

Key: 0 4 represents 4 free throws



5. How many classmates said they spend morethan 20 minutes and less than 40 minutesdoing chores in a week?


7. How many classmates said they do not spendany time doing chores in a week?


Minutes Spent Doing ChoresStem Leaves

2 2 2 4 63 0 5 5 84 0 65 5 86 27 1 4

Key: 0 4 represents 4 free throws


GRADE 4Open-Ended


TEKS CATEGORY 6Personal Financial

Literacy

®MATHEMATICS





Serena makes sock puppets to earn money to donateto the Theater Club. The items she bought to makethe puppets and the cost of each item is shown.

Item Cost1 pair of craft scissors $10.996-pairs of white socks $2 per pair3 yards of felt fabric(1 yd. red, 1 yd. pink, 1 yd. black)

$6 per yard

Bottle of craft glue $5.99Assorted buttons $3.7910-pack of colored cardboard $5.43

Each sock makes one puppet. Serena will use all ofthe socks to make puppets. She will sell each sockpuppet for $8. Find out if Serena will make a profit ifshe sells all of the puppets.

First, find the total amount of her expenses.

1. Find the total amount paid for the socks. Showyour work.

2. What is the total amount paid for the socks?

3. Find the total amount paid for felt. Show yourwork.

4. What is the total amount paid for the felt?

5. Find the total amount of Serena’s expenses.Show your work.

6. What is the total amount of Serena’s expenses?



Next, find the amount Serena received from sellingthe puppets.

7. Find the total number of puppets she made if sheused all of the socks. Show your work.

8. What is the total number of puppets she made?

Finally, find the amount of Serena’s profit.

9. Find the difference between Serena’s expensesand the amount she received from selling thepuppets. Show your work.

10. What is the amount of Serena’s profit?

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